We define a Jordan analogue of Lambek and Utumi's associative algebra of quotients and we construct the maximal algebra of quotients for nondegenerate Jordan algebras. We apply those results to other classes of algebras of quotients appearing in the literature.

In this paper, we give a classification of Lie bialgebra structures on Lie algebras of type g[[x]] and g [x], where g is a simple complex finite dimensional Lie algebra.

In this paper we study Jordan algebras having nonzero local algebras that satisfy the property of being Lesieur-Croisot (i.e., being orders in nondegenerate Jordan algebras of finite capacity). We will prove that the set of the elements of a nondegenerate Jordan algebra at which the local algebra is Lesieur-Croisot is an ideal.

In this paper we study Jordan systems having nonzero local algebras that satisfy a polynomial identity. We prove that in nondegenerate Jordan systems the set of elements at which the local algebra is PI is an ideal and that if it is nonzero, it coincides with the socle when the system is primitive. ᮊ

No abstract